Take your car to a local motorfactors and ask them to test the battery - they have a nasty habit of failing in cold weather.
Starter motors, by contrast, tend to quite like cold weather (although can obviously fail at any time).
From the sounds of it, you actually may not have a problem at all - its just your car isn't running for long enough to keep the battery fully charged (16 miles after a hard start isn't far).
You can get portable battery chargers, for example, click here
If you go down this route, make sure you recharge the recharger over night.